On form-factor expansions for the XXZ chain in the massive regime

We study the large-volume-$L$ limit of form factors of the longitudinal spin operators for the XXZ spin-$1\mathrm{/}2$ chain in the massive regime. We find that the individual form factors decay as $L^{-n}$, $n$ being an even integer counting the number of physical excitations – the holes – that constitute the excited state. Our expression allows us to derive the form-factor expansion of two-point spin-spin correlation functions in the thermodynamic limit $L\to +\mathrm{\infty }$. The staggered magnetisation appears naturally as the first term in this expansion. We show that all other contributions to the two-point correlation function are exponentially small in the large-distance regime.